Constructor Function
The Constructor Function is an uncomputable function. Definition: \(C(0)=0\) (null program) \(C(n)=\)Largest returned value of JavaScript (ECMAScript 7) program of length \(\leq C(n-1)+1\) If a JS program is being used to calculate \(C(n)\), the JS program can use \(C(m)\) iff \(m\lt n\) (That is, the program for the smaller \(C(m)\) can be included in the program. Afterall, it is still a part of the permutation of programs). return Infinity doesn't count. For example: If a program is being used to calculate \(C(6)\), then \(C(5)\), \(C(4)\), etc. can be used in the program, but \(C(6)\), \(C(7)\), etc. since it wouldn't fit inside the character limit. The final value calculated by the program is the return value. C(0)=0 C(1)=9 C(2)=9**9**9**9 C(3)>BB(100) C(4)>BIG FOOT C(x) is at least BB(BB(BB(...(x)...))) with x BBs The lower bound is most likely \(f(\omega_{1}^{CK}+1)\) According to User:Cool and good and cool, \(C(C(3))\) is one of the largest googolisms of all time, and it may even pass Oblivion. The Constructor Function has an Uncomputability Level of 2. Growth rate is most likely something near \(\omega_{\omega_{1}^{CK}}^{CK}\). Reasoning: Uncomputability Level 1 Function (Busy Beaver-like function): \(\omega_1\)^CK Uncomputability Level 2 Function: \(\omega_{\omega_{1}^{CK}}^{CK}\) KNOWN VALUES \(C(0)=0\) because the only 0-length program is the null program, which (in a way) returns 0. \(C(1)=9\) using the following: 9 \(C(2)\geq9^{9^{9^9}}\), maybe using the following (most likely the largest): 9**9**9**9 \(C(3)\) is probably much larger than \(BB(10^{10^{70}})\) using a Turing Machine emulator. This is because the Busy Beaver machine for a very large number of states could be stored in some sort of compressed state, which is decompressed repeatedly and run. FE OLD EXTENSION TO THIS THING So suppose we have JS program working with set theory now lets call perm1 as language that can describe anything in this language with 1 symbol. Sol it have all permutations as the number of symbols, e.g. If it was 1 and 2 language and 2 symbols length perm1 would have 1 symbol for 1 for 2 for 12 for 11 for 21 for 22 eg 1 is still 1 (we dont need new symbol), and 2, q 1 is 12, w is 11, e is 21, r is 22 so largest number with permC(C...(C(999))...) WITH C(C(C(999))) C'S language WRITTEN WITH C(C(C(999))) SYMBOLS = PRETTYNUMBER Extension by User:Cool and good and cool and User:C7X Another extension. This extends the Constructor Function to 2 arguments. \(C(a,0)=0\) (null program) \(C(0,n)=n\) \(C(1,b)=\)Largest returned value of JavaScript (ECMAScript 7) program of length \(\leq n\) \(C(a,b)=\)Largest returned value of JavaScript (ECMAScript 7) program of length \(\leq C(a-2,C(a,b-1)+1)\) Calculations of \(C(a,b)\) can use \(C(m,n)\) for \(m2 Function CC(x) = largest possible return value using ONLY CONSTRUCTOR FUNCTION and x characters superscript symbol ^ (indicating repetition) does not count as a character, but parentheses do values for CC(1) # 9 # 99 # 999 # C(9) # C9(9) # C99(9) # C999(9) # CC(9)(9) and so on. Extension by User:Maxywaxy 2 Super Constructor function \(SC(0)\) = \(C(10^{100})\) \(SC(n+1)\) = \(C^{SC(n)}(SC(n))\) example: \(SC(1)\) = \(C^{C(10^{100})}(C(10^{100}))\) It is sort of a salad function \(SC(10^{100})\) = Superstructor Category:FUNCTIONS Category:POTENTIALLY WELL-DEFINED Category:Uncomputable Functions Category:C7X's Stuff Category:Computer Science Related Functions